10,178 research outputs found
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation
In this paper, we present the optimization formulation of the Kalman
filtering and smoothing problems, and use this perspective to develop a variety
of extensions and applications. We first formulate classic Kalman smoothing as
a least squares problem, highlight special structure, and show that the classic
filtering and smoothing algorithms are equivalent to a particular algorithm for
solving this problem. Once this equivalence is established, we present
extensions of Kalman smoothing to systems with nonlinear process and
measurement models, systems with linear and nonlinear inequality constraints,
systems with outliers in the measurements or sudden changes in the state, and
systems where the sparsity of the state sequence must be accounted for. All
extensions preserve the computational efficiency of the classic algorithms, and
most of the extensions are illustrated with numerical examples, which are part
of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure
Decentralized sequential change detection using physical layer fusion
The problem of decentralized sequential detection with conditionally
independent observations is studied. The sensors form a star topology with a
central node called fusion center as the hub. The sensors make noisy
observations of a parameter that changes from an initial state to a final state
at a random time where the random change time has a geometric distribution. The
sensors amplify and forward the observations over a wireless Gaussian multiple
access channel and operate under either a power constraint or an energy
constraint. The optimal transmission strategy at each stage is shown to be the
one that maximizes a certain Ali-Silvey distance between the distributions for
the hypotheses before and after the change. Simulations demonstrate that the
proposed analog technique has lower detection delays when compared with
existing schemes. Simulations further demonstrate that the energy-constrained
formulation enables better use of the total available energy than the
power-constrained formulation in the change detection problem.Comment: 10 pages, two-column, 10 figures, revised based on feedback from
reviewers, accepted for publication in IEEE Trans. on Wireless Communication
Output feedback stable stochastic predictive control with hard control constraints
We present a stochastic predictive controller for discrete time linear time
invariant systems under incomplete state information. Our approach is based on
a suitable choice of control policies, stability constraints, and employment of
a Kalman filter to estimate the states of the system from incomplete and
corrupt observations. We demonstrate that this approach yields a
computationally tractable problem that should be solved online periodically,
and that the resulting closed loop system is mean-square bounded for any
positive bound on the control actions. Our results allow one to tackle the
largest class of linear time invariant systems known to be amenable to
stochastic stabilization under bounded control actions via output feedback
stochastic predictive control
On the interpretation and identification of dynamic Takagi-Sugenofuzzy models
Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples
- …